Browsing Algebraic Combinatorics by Title

We present a procedure for amalgamating a net and a collection of designs into a single design. At first this amalgam is just point-regular, but it acquires additional regularities upon imposing restrictions on the ...

This paper gives an explicit value for the dimension of the code of a strongly resolvable design over the field of prime order $p$ in the case when $p$ is not a divisor of $k-\rho$, where $k$ is the block size of the design ...

This paper establishes a correspondence between mutually orthogonal frequency squares (MOFS) and nets satisfying an extra property (“framed nets”). In particular, we provide a new proof for the bound on the maximal size ...

The hulls of codes from the row span over F_p, for any prime p, of incidence matrices of connected k-regular graphs are examined, and the dimension of the hull is given in terms of the dimension of the row span of A+kI ...

We determine information sets for the generalized Reed–Muller codes and use these to apply partial permutation decoding to codes from finite geometries over prime fields. We also obtain new bases of minimum-weight vectors ...

Until recently, the known symmetric nets were class-regular and therefore satisfied a certain geometric condition that defines the class of nets known as tactical symmetric nets. Thus the known symmetric nets were tactical. ...

Rahilly [On the line structure of designs, Discrete Math. 92 (1991) 291–303] described a construction that relates any Hadamard design H on 4^m-1 points with a line spread to an affine design having the same parameters as ...

Given an involution z in W, where W is the symmetric group of degree n, we study the relation between the subsystems of a root system for W corresponding to certain decreasing subsequences of z and the two-sided Kazhdan–Lusztig ...

We study the relation between certain increasing and decreasing subsequences occurring in the row form of certain elements in the symmetric group, following Schensted [C. Schensted, Longest increasing and decreasing ...

Explicit PD-sets are found for partial permutation decoding of the generalized Reed-Muller codes from the affine geometry designs of points and lines in dimension 3 over the prime field of order p, using the information ...

We show that a quasi-symmetric design with intersection numbers 1 and y > 1 and a good block belongs to one of three types: (a) it has the same parameters as PG 2(4, q), the design of points and planes in projective 4-space; ...

We show that the first- and second-order Reed–Muller codes, and , can be used for permutation decoding by finding, within the translation group, (m−1)- and (m+1)-PD-sets for for m≥5,6, respectively, and (m−3)-PD-sets for ...

We show that a construction described in [K.L. Clark, J.D. Key, M.J. de Resmini, Dual codes of translation planes, European J. Combinatorics 23 (2002) 529–538] of small-weight words in the dual codes of finite translation ...